54. If h(x) = √√/4 + 3ƒ(x), where ƒ(1) = 7 and ƒ'(1) = 4, find hʼ(1).

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

A:

Q: Estimate the slope of the tangent to the function… at the point of abscissa -3 and then determine…

A:

Q: What is the equation of the line tangent to * f(x) = 4x2 + 2x – 1 at x = 0

A:

Q: Find the values of x for which  f(x)=(1/3)x3 +(5/2)x2 +6x-17 Has a tangent line that is parallel…

A: As the line is parallel, slope of them will be equal. Slope of f(x)=x33+5x22+6x-17 will be :…

Q: Find the inflection point of the curve f(x)=2x³ – 18x²+ 30x. О а.3 O b. 3/2 С. 9 O d. None

A: We have to find out point of inflection

Q: Find the equation of the tangent to the curve at x = 3 for the function: f(x) = [(2x+1)³ (4x-3)

A:

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: The derivative of f(x) = In(5x³ – 12) Is

A:

Q: The height of a sand dune (in centimeters) is represented by f(t) = 850 - 2t² cm, where t is…

A: Given the height of the sand dune is represented by f(t)=850-2t2 cm where t is measured in years…

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: 3. Find the intersection point of the tangents to the graph of the function f(x)=√x² + 3x + 6 in the…

A: To determine the intersection point of two tangents on the given curve.

Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: B6. Express + ar

A: Given

Q: Sketch the curve y=sin(x)/(1+cos(x)).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2. Find when f(x) = x²e* has a horizontal tangent.

A:

Q: Q#2. By definition find derivative of (2x+3)/4.

A:

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given: